What is the best coilover? Best brake pads? Best springs? Best sways? etc etc.

Disclaimer: this is meant to be general (i.e. wild overgeneralization). If there are any factual problems, let me know.

The goal of this is two-fold:
1) Take some of the load off of the Gurus so they don't have to repeat the same junk every five minutes
2) Make sure people don't buy more stuff than they really need

If you really want a BBK, or coilovers, even though all you do is drive down the street to buy groceries... more power to you. But you don't need to. If you aren't sure if you want one, this can help you decide.

First of all, realize that you are starting with a car that already handles pretty well. The RS, WRX and STi are all reasonably potent cars with a good set of tires.

"What are some of the best bang-for-buck handling mods I can do?"

0. Driving school, autocross entry fees, track days, and other things that will make you a better driver. The good driver in the bad car will always smoke the bad driver in the good car. There are plenty of drivers on this forum that can whoop you in your coilovered STi with a stock RS. With sufficient practice, you can be one of those people And then the money you spend on suspension will be worth it, because you will be able to get immediate meaningful feedback about how your suspension changes are affecting handling.

1. Tires. Your tires are the only part of your car that touches the road. If you can afford to run two sets of tires, or if you live in warm weather all year long, run a good set of summer tires. Be warned that with good, stiff-sidewall tires comes road noise and decreased ride quality. If you buy a bunch of suspension mods, an expensive set of coilovers, etc, and then buy mushy all season tires or some "tuner" tire that doesn't have particularly good sidewalls, you are probably wasting the money you spent on suspension parts. You can do this without TOUCHING your suspension or voiding your warranty or anything like that.

2. An alignment. You want to research this first, but if you are not buying camber bolts or plates, try to go with as much negative camber as you can evenly get in the front, and as little as you can get in the rear (again, GENERAL rules).

You can control a lot of understeer/oversteer balance this way. A lot of people who install shiny new coilovers who say "holy crap my car handles great now" might actually be raving about the alignment moreso than the coilovers. A properly set-up strut/spring combo, with camber plates and an aggressive alignment, can be an effective weapon. Only fiddle with toe if you know what you're doing.

Most importantly - alignments are CHEAP! The most expensive alignment I've ever seen was $200, which is a lot, but still cheaper than just about any other suspension mod you can do. The flipside: if you are going to try to make your car handle better, you are fighting gravity unless you go with a matching alignment. You don't want to be driving on the sidewalls of your front tires under load. That = understeer city and horrible noises.

2a. Camber bolts, for the same reason as an alignment. They're cheap.

3. Swaybars. Pick some that are appropriately sized for your application. As Jim/ITWRX4ME points out, make sure you know what lift throttle oversteer is, how to cause it, and more importantly how NOT to cause it before you start dabbling.

4. Once we get here, you may be ready to swap out your stock struts and springs.

"My STi understeers! I turn the wheel and the car doesn't turn! I just hear this horrible screeching noise? I thought this was a JGTC car, what gives?"

Understeer can be dialed out lots of ways.
-Driving style. This is hands down the biggest one. If you are going WOT and yank the wheel it's very possible to get it to plow. "Slow in, fast out" can get rid of a lot of driver-induced understeer.
-Tire pressure. If you are on RE92's and you are experiencing understeer, add pressure Most tires have sissy-la-la sidewalls and without a lot of air you will be driving on the sidewalls under hard cornering. Try jacking up the pressure in the rear higher than the fronts and see how you like it.
-Alignment. See above: find one for your application.
-Actual suspension modifications

"I want to do track days, rallycross, autocross, and also daily drive. What should I do?"

It's really really hard to find a setup that will be good at all of these. The optimal setups for all of these are all different.

Fred (that's his username) has a lot of experience doing both rallycross and autox on the same suspension. Those are probably the hardest two to combine, so search for his posts on the subject (like this one). He is currently running a set of Tein HG's IIRC. BIGSKYWRX also has a "compromise" suspension. One post of his about it is here

The STi suspensions in general are very good all around, just not specialized for one thing - which is fine, if you are not trying to specialize either.

My personal opinion - pick the one you like the most. Prep your Subaru for that. If you still want to do the other ones, buy a beater. You don't need a 300 hp AWD car to enjoy rallycross! And you don't need one for autox or track days either. You can have a front wheel drive beater rally car (Neon? Old 2WD Subaru? Old VW?), or buy a cheap rear wheel drive beater track car (Miata? Old BMW?)... etc etc.

If you want to specialize, you'll know

I hope this helps some people. It's definitely not a Unabomber-class FAQ, more like a series of starting points. Feedback appreciated; I don't pretend to know all this stuff.